1 / (1 + 1 / (1 – 1/x)) = 4, x = ?
We can follow outside to inside method to solve this type of problems. x is in the inner part of this fraction; then, we need to narrow the circle to reach x:
1 / (1 + 1 / (1 – 1/x)) = 4
This means that (1 + 1 / (1 – 1/x)) is equal to 1/4.
Then,
1 + 1 / (1 – 1/x) = 1/4
1 / (1 – 1/x) = 1/4 – 1
1 / (1 – 1/x) = – 3/4
This means that 1 – 1/x = – 4/3. Then,
1 – 1/x = – 4/3
1 + 4/3 = 1/x
1/x = 7/3
So,
x = 3/7.